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Equations for sensitivity coefficients of eigenvalue-difference responses such as reactivity are derived from a unified approach based on both eigenvalue and generalized perturbation theory. The sensitivity coefficients are utilized for uncertainty analysis of reactivity responses, and it is shown that these types of responses have inherently larger relative uncertainties than eigenvalue responses. Monte Carlo calculations are used to apply the methodology to the analysis of the coolant void reactivity in a three-dimensional model of a fuel bundle in an advanced CANDU reactor system. The important data sensitivities are identified, and it is shown that the coolant void reactivity has a large uncertainty due to nuclear data uncertainties.